Multihypothesis threat missile propagator for boost-phase missile defense
A fire control system for a boost phase threat missile includes sensors for generating target-missile representative signals, and a multi-hypothesis track filter, which estimates the states of various target hypotheses. The estimated states are typed to generate hypotheses and their likelihoods. The states, hypotheses and likelihoods are applied to a multihypothesis track filter, and the resulting propagated states are applied to an engagement planner, together with the hypotheses and likelihoods. The engagement planner initializes the interceptor(s). Interceptor guidance uses the initialization and the propagated states and typing information to command the interceptor.
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This invention relates to defense against ballistic missiles in their boost phase, and more particularly to arrangements for propagating threat missile states during the boost phase.
BACKGROUND OF THE INVENTIONDefenses against ballistic missiles are currently concentrating upon the boost phase of the ballistic missile, which is a phase at which multiple warheads and/or countermeasures have not as yet been deployed. Intercepting a ballistic missile before it can deploy complicated countermeasures and/or multiple warheads greatly decreases the burden on sensors to distinguish lethal payload object(s) from countermeasures. The concept involves having interceptor assets at a location near the expected launch sites of threatening offensive ballistic missiles, sensing the presence of the threat missile soon after launch, calculating its expected trajectory, and launching interceptor asset(s) to intercept the threat missile. It will be understood that initially, a defender sensing the launch of a ballistic missile does not know exactly when it was launched, the type of missile which has been launched (although there may be some knowledge of the missile types available at the launch site), its mass, thrust, and intended trajectory. In fact, very little is initially known. Unlike engagements of threat missiles in their mid-course phase, where the trajectory of such threat missiles is well defined by Keplerian orbits, uncertainty in the trajectory of a boosting missile is a major factor in defeating such a threat missile.
Defeating threat missiles in their boost phase requires methods to filter sensor measurements and establish track states, to determine the type of a threat missile, to propagate the threat missile's state into the future, to plan an engagement against a threat missile, and to guide an interceptor to destroy the threat missile. An engagement planner for boost phase intercepts must weigh the capability of the interceptor against the uncertainty in the trajectory of the boosting threat missile.
The problem of defense against a boosting threat missile is further exacerbated by the lack of knowledge of the threat missile's trajectory, as one can only plan an interceptor missile launch if one knows which interceptor missile, among several, is in a position from which it can be expected to make a successful interception.
Missile defense arrangements that are adequate for engaging threat missile(s) in its (their) mid-course phase may not be adequate for engaging threat missiles in their boost phase. Improved or alternative boost phase missile defense arrangements are desired.
SUMMARY OF THE INVENTIONA method for boost phase target propagation according to an aspect of the invention comprises the steps of sensing a target to produce target-representative signals representing at least target position, and applying the target-representative signals to a multi-hypothesis filter for producing at least smoothed position, velocity, and mass flow rate information defining the state of the target. Target acceleration is predicted from the smoothed position, velocity, and mass flow rate information using the rocket equation, to thereby produce predicted acceleration. The predicted acceleration is integrated to generate estimated missile position and velocity representing the propagated missile states.
A method according to an aspect of the invention is for boost phase target propagation. The method comprises the step of sensing a target missile to produce target-representative signals representing at least target missile position. The target-representative signals are applied to a multi-hypothesis filter for producing a state vector of the target missile containing at least position and velocity information defining the state of the target missile. The time derivative of the state vector of the target missile is computed using the rocket equation. The time derivative of the state vector is integrated, preferably by numerical integration, to generate estimated target missile position and velocity representing the propagated missile states. In a particular mode of the method, the step of applying the target-representative signals to a multi-hypothesis filter for producing a state vector of the target missile containing at least position and velocity information defining the state of the target missile comprises the step of determining the state vector as
In another mode of the method, the step of using the rocket equation to compute the time derivative of the state vector of the target missile includes the step of calculating
In another mode of the invention, the step of integrating the time derivative of the state vector to generate estimated target missile position and velocity representing the propagated missile states includes the step of calculating
According to another aspect of the invention, a method for propagating trajectories of a boosting target missile comprises the step of, for each of a plurality of hypotheses of target missile type and stage, generating estimates of at least target missile velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), specific mass flow rate ({dot over (M)}), time until burnout of the current target missile stage, and specific impulse (ISP), and for each of the plurality of hypotheses, propagating the target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage, with the assumption being made that the target kinematics are expressed by:
where
{umlaut over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
{dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
Z(t) is the target position vector (Earth-fixed reference frame);
μ is the Earth gravitational constant;
ω is the Earth angular velocity vector;
Isp is the specific impulse of the target rocket motor;
gc is the standard gravitational acceleration at Earth's equator; and
b(t) is the specific mass flow vector of target rocket motor,
and the target state is expressed as a vector containing at least target position, velocity, specific mass flow rate, and acceleration
and the derivative of such a vector can be expressed as:
and the propagation to the end of the current stage is performed by integrating the equation
where the integration may be a numerical integration using a technique such as a fourth order Runge-Kutta scheme. In a particular mode of this method, the step of propagating the target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage includes the step of integrating equation (5) to the end of the current stage, deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, and if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter, and if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage. The steps of (a) deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, (b) if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter and (c) if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage are repeated as needed. In a preferred mode of the method, the step of propagating the target hypothesis/stage combination includes the step of, while propagating the hypothesis to the end of the current stage, through subsequent stages, and for a ballistic portion of flight, saving the propagated target state at points sufficiently close in time to completely represent the target trajectory, and making the propagated and saved target states available as the output of the method. Sufficiently close in time in one mode is one second.
A method according to another aspect of the invention for propagating trajectories of a boosting target missile comprises the step of generating estimates of at least target missile velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), and launch time, and for each of a plurality of hypotheses of target missile type and stage, obtaining at least the nominal target missile parameters of staging times, specific mass flow rate ({dot over (M)}), specific thrust (ISP), and angle of attack (AoA). The method also includes the step of, for each of a plurality of hypotheses of target missile type and stage, computing from the estimated target missile velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), and launch time, and from the nominal target missile parameters, an estimate of the current stage, and of the time until burnout of the current stage. A determination is made, from the estimates of current stage and time until burnout of current stage the time since ignition of the current stage and the specific mass flow rate {dot over (M)} at the current time for the target/stage combination. For each of the plurality of hypotheses, the target hypothesis/stage combination is propagated to a time corresponding to the estimated end time of the current stage. In one version of this method, the assumption is made that the target kinematics are expressed by:
where
{dot over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
{dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
Z(t) is the target position vector (Earth-fixed reference frame);
μ is the Earth gravitational constant;
ω is the Earth angular velocity vector;
Isp is the specific impulse of the target rocket motor;
gc is the standard gravitational acceleration at Earth's equator; and
b(t) is the specific mass flow vector of target rocket motor,
and that the target state is expressed as a vector containing at least target position, velocity, specific mass flow rate, and acceleration
and that the derivative of such a vector can be expressed as:
In this method, the propagation to the end of the current stage is made by integrating the equation
The integration can be performed by using a numerical integration technique such as a fourth order Runge-Kutta scheme. In one mode of the method, the step of integrating equation (5) to the end of the current stage includes the step of deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, and if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter. In another mode of the invention, the step of integrating equation (5) includes the step of, if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage, and repeating the steps of (a) deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, (b) if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter and (c) if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage. In a mode of this method, the step of, for each of a plurality of hypotheses of target missile type and stage, computing the time until burnout of the current stage comprises the steps of subtracting the current time from the estimated launch time, and comparing the resulting estimate of time since target launch to the nominal target timeline for the hypothesis to indicate the stage of the hypothesis. In another mode of this method, the step of propagating the estimated position and velocity of the target missile to the estimated time of the end of the current stage, through subsequent stages, and for a ballistic portion of flight, includes the step of saving the propagated target state at points sufficiently close in time to completely represent the target trajectory, and in one version the propagated target missile states at one-second intervals are saved. In another mode of this method, the step of propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter comprises the step of propagating the states until a selected time after lift off (TALO).
In operation of the arrangement of
In operation of the arrangement of
The operation of the logic 300 of
The track filter states from track filter block 312 of
The propagated multihypothesis threat states from target propagator block 316 of
Interceptor guidance block 320 of
Block 722 in
The assumption is made in the calculations of block 714 that the target acceleration obeys the standard rocket equation
where:
{umlaut over (x)} is acceleration;
Isp is specific impulse;
gc is the force of gravity;
{dot over (m)} is the mass flow rate; and
m is the target mass.
Additionally, in order to derive the filter dynamics equations, it is assumed that the target's specific impulse Isp is constant. Also, due to the high altitudes at which the propagation takes place, the algorithms of block 714 assume that the rocket pressure correction (pressure thrust) and atmospheric drag are negligible. Given these assumptions, the following equations (2), (3), (4) and (5) describe the assumed boost phase target propagator (BPTP) target kinematics:
where
{dot over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
{dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
Z(t) is the target position vector (Earth-fixed reference frame);
μ is the Earth gravitational constant;
ω is the Earth angular velocity vector;
Isp is the specific impulse of the target rocket motor;
gc is the standard gravitational acceleration at Earth's equator; and
b(t) is the specific mass flow vector of target rocket motor,
all as described in more detail in copending U.S. patent application Ser. No. 10/972,943 filed on Oct. 25, 2004 in the name of Boka et al. and entitled “Computerized Method for Generating Low-Bias Estimates of Position of a Vehicle From Sensor Data,” now U.S. Pat. No. 7,181,323, issued on Feb. 20, 2007. This patent describes a boost filter, the Unified Unbiased Rocket Equation Extended Kalman Algorithm (UUREEKA), which estimates current states.
The Boost Phase Target Propagator (BPTP) state vector determined in block 714 of
The derivative of the state vector is
Time propagation of the BPTP state vector is performed by numerically integrating the state derivative vector equations (4):
Any appropriate numerical integration technique, such as a fourth-order Runge-Kutta, can be used. Propagator 714 of
Decision block 715 of
The output of block 724 of page 716a of
The boost phase target missile propagator 316 of
The boost phase target propagator of
Block 727 in
Integrator block 726 in
Decision block 731 of
The output of block 730 of page 736a of
The boost phase target missile propagator 316 of
When a final target hypothesis is reached, decision block 810 of
where:
-
- FoMCOMP is the composite FoM;
FoM is the opportunity FoM for each combination of intercept time, interceptor flyout strategy, and target hypothesis;
LH is the likelihood of a target hypothesis being correct; and
n is the number of target hypotheses to consider.
The likelihood LH is received from a typing algorithm, such as typing block 314 of
When the composite FoM is calculated in block 818 of
In the logic of
where
Ā is a propagated threat missile acceleration for one hypothesis;
ĀBET is the best estimated threat missile acceleration.
Integrating the interceptor states has the advantage of reducing approximation of the interceptor flyout. The heading error is determined by finding an initial (optimal) heading that results in a near zero miss distance (the distance between the interceptor and threat missile BET at the point of closest approach). The computations determine the optimal heading and heading error each time the algorithm is called. The heading error is the difference between the current interceptor heading and the interceptor heading which would result in intercepting the target without further guidance commands. The boost phase interceptor guidance arrangement of
Where:
κ=Constant=3.0
VMSL=Missile velocity
λ=Heading error
Tgo=Time to go till end of control
Acc=Magnitude of acceleration command
In
A method (300,316) for boost phase target propagation according to an aspect of the invention comprises the steps of sensing a target (310) to produce (312) target-representative signals representing at least target position, and applying the target-representative signals to a multi-hypothesis filter (316) for producing at least position ({circumflex over (X)}mi), velocity ({circumflex over (V)}mi), and mass flow rate ({dot over (M)}) information defining the state of the target. The derivative of the target state vector is calculated from the smoothed position ({circumflex over (X)}mi), velocity ({circumflex over (V)}mi), and mass flow rate ({dot over (M)}) information (in the form of a state vector, equation 3) using equation (4). The state vector at a future time is determined by evaluating equation (5).
A method according to an aspect of the invention is for boost phase target propagation. The method comprises the step of sensing (310) a target missile (225a, 225b) to produce target-representative signals representing at least target missile (225a, 225b) position. The target-representative signals are applied to a multi-hypothesis filter (312) for producing a state vector (equation 3) of the target missile (225a, 225b) containing at least position and velocity information defining the state of the target missile (225a, 225b). The time derivative (equation 4) of the state vector (equation 3) of the target missile (225a, 225b) is computed using the rocket equation (equation 1). The time derivative (equation 4) of the state vector (equation 3) is integrated (equation 5), preferably by numerical integration, to generate estimated target missile (225a, 225b) position and velocity representing the propagated missile states. In a particular mode of the method, the step of applying the target-representative signals to a multi-hypothesis filter (312) for producing a state vector (equation 3) of the target missile (225a, 225b) containing at least position and velocity information defining the state of the target missile (225a, 225b) comprises the step of determining the state vector as
In another mode of the method, the step of using the rocket equation (equation 1) to compute the time derivative of the state vector of the target missile (225a, 225b) includes the step of calculating
In another mode of the invention, the step of integrating the time derivative of the state vector to generate estimated target missile (225a, 225b) position and velocity representing the propagated missile states includes the step of calculating
According to another aspect of the invention, a method for propagating trajectories of a boosting target missile (225a, 225b) comprises the step of, for each of a plurality of hypotheses of target missile (225a, 225b) type and stage, generating estimates of at least target missile (225a, 225b) velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), specific mass flow rate ({dot over (M)}), time until burnout of the current target missile (225a, 225b) stage, and specific impulse (ISP), and for each of the plurality of hypotheses, propagating (block 714) the target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage, with the assumption being made that the target kinematics are expressed by:
where
{umlaut over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
{dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
Z(t) is the target position vector (Earth-fixed reference frame);
μ is the Earth gravitational constant;
ω is the Earth angular velocity vector;
Isp is the specific impulse of the target rocket motor;
gc is the standard gravitational acceleration at Earth's equator; and
b(t) is the specific mass flow vector of target rocket motor,
and the target state is expressed as a vector containing at least target position, velocity, specific mass flow rate, and acceleration
and the derivative of such a vector can be expressed as:
and the propagation to the end of the current stage is made by integrating the equation
where the integration may be a numerical integration using a technique such as a fourth order Runge-Kutta scheme. In a particular mode of this method, the step of propagating (block 714) the target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage includes the step of integrating equation 5 to the end of the current stage, deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, and if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter, and if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage. The steps of (a) deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, (b) if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter and (c) if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage are repeated as needed. In a preferred mode of the method, the step of propagating the target hypothesis/stage combination includes the step of, while propagating the hypothesis to the end of the current stage, through subsequent stages, and for a ballistic portion of flight, saving the propagated target state at points sufficiently close in time to completely represent the target trajectory, and making the propagated and saved target states available as the output of the method. Sufficiently close in time in one mode is one second.
A method according to another aspect of the invention for propagating trajectories of a boosting target missile (225a, 225b) comprises the step of generating estimates (310) of at least target missile (225a, 225b) velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), and launch time, and for each of a plurality of hypotheses of target missile (225a, 225b) type and stage, obtaining (727) at least the nominal target missile (225a, 225b) parameters of staging times, specific mass flow rate ({dot over (M)}), specific thrust (ISP), and angle of attack (AoA). The method also includes the step of, for each of a plurality of hypotheses of target missile (225a, 225b) type and stage, computing (725) from the estimated target missile (225a, 225b) velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), and launch time, and from the nominal target missile (225a, 225b) parameters, an estimate of the current stage, and of the time until burnout of the current stage. A determination is made (726), from the estimates of current stage and time until burnout of current stage the time since ignition of the current stage and the specific mass flow rate {dot over (M)} at the current time for the target/stage combination. For each of the plurality of hypotheses, the target hypothesis/stage combination is propagated (block 728) to a time corresponding to the estimated end time of the current stage. In one version of this method, the assumption is made that the target kinematics are expressed by:
where
{umlaut over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
{dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
Z(t) is the target position vector (Earth-fixed reference frame);
μ is the Earth gravitational constant;
ω is the Earth angular velocity vector;
Isp is the specific impulse of the target rocket motor;
gc is the standard gravitational acceleration at Earth's equator; and
b(t) is the specific mass flow vector of target rocket motor,
and that the target state is expressed as a vector containing at least target position, velocity, specific mass flow rate, and acceleration
and that the derivative of such a vector can be expressed as:
In this method, the propagation to the end of the current stage is made by integrating the equation
The integration can be performed by using a numerical integration technique such as a fourth order Runge-Kutta scheme. In one mode of the method, the step of integrating equation (5) to the end of the current stage includes the step of deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, and if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter. In another mode of the invention, the step of integrating equation (5) includes the step of, if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage, and repeating the steps of (a) deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, (b) if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter and (c) if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage. In a mode of this method, the step of, for each of a plurality of hypotheses of target missile (225a, 225b) type and stage, computing (725) the time until burnout of the current stage comprises the steps of subtracting the current time from the estimated launch time, and comparing the resulting estimate of time since target launch to the nominal target timeline for the hypothesis to indicate the stage of the hypothesis. In another mode of this method, the step of propagating the estimated position and velocity of the target missile (225a, 225b) to the estimated time of the end of the current stage, through subsequent stages, and for a ballistic portion of flight, includes the step of saving the propagated target state at points sufficiently close in time to completely represent the target trajectory, and in one version the propagated target missile states at one-second intervals are saved. In another mode of this method, the step of propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter comprises the step of propagating the states until a selected time after lift off (TALO).
Claims
1. A method for boost phase fire control, said method comprising the steps of:
- sensing a target missile to produce target-representative signals representing at least target position;
- applying said target-representative signals to a multi-hypothesis filter for producing a state vector of the target missile containing at least position and velocity information defining the state of said target missile;
- using a rocket equation, computing the time derivative of said state vector of the target missile;
- integrating said time derivative of said state vector to generate estimated target missile position and velocity representing propagated target missile states; and
- guiding an interceptor to the target missile using the propagated missile states.
2. A method according to claim 1, wherein said step of applying said target-representative signals to a multi-hypothesis filter for producing a state vector of the target containing at least position and velocity information defining the state of said target missile comprises the step of determining the state vector as s _ ( t ) = { Z _ ( t ) Z. _ ( t ) b _ ( t ) A _ ( t ) }.
3. A method according to claim 1, wherein said step of using the rocket equation, computing the time derivative of said state vector of the target missile includes the step of calculating s. _ ( t ) = { Z. _ ( t ) Z ¨ _ ( t ) b. _ ( t ) A. _ ( t ) } = { Z. _ ( t ) - μ Z _ ( t ) Z _ ( t ) 3 + A ( t ) b _ ( t ) b _ ( t ) - ω x ( Z _ ( t ) ) - 2 ω x Z. _ ( t ) b _ ( t ) b _ ( t ) A ( t ) b _ ( t ) }.
4. A method according to claim 1, wherein said step of integrating said time derivative of said state vector to generate estimated target missile position and velocity representing the propagated missile states includes the step of calculating s _ ( t + Δ t ) = s _ ( t ) + ∫ t t + Δ t s. _ ( s _ ( t ) ) ⅆ t.
5. A method for intercepting a boosting target missile, said method comprising the steps of:
- for each of a plurality of hypotheses of target missile type and stage, generating estimates of at least target missile velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), specific mass flow rate ({dot over (M)}), time until burnout of a current target missile stage, and specific impulse (ISP);
- for each of said plurality of hypotheses, propagating a target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage;
- deciding if the end of the current stage corresponds to the end of a last stage of the hypothesis;
- if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter; and
- guiding an interceptor to the boosting target missile using the propagated states of the hypothesis.
6. A method according to claim 5, further comprising, after said step of: if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter, the steps of;
- if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage, and repeating said steps of (a) deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, (b) if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter and (c) if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage.
7. A method according to claim 5, wherein said step of propagating the target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage is made with the assumptions being made that the target kinematics are expressed by: Z ¨ _ ( t ) = - μ Z _ ( t ) Z _ ( t ) 3 + A _ ( t ) - ω _ × ( ω _ × Z _ ( t ) ) - 2 ω _ × Z. _ ( t ) [ gravity ] [ thrust ] [ centerfugal ] [ coriolis ] A _ ( t ) = I sp g c b _ ( t ) A ( t ) = A ( t ) b. _ ( t ) = b ( t ) · b _ ( t ) where s _ ( t ) = { Z _ ( t ) Z. _ ( t ) b _ ( t ) A _ ( t ) } s. _ ( t ) = { Z. _ ( t ) Z ¨ _ ( t ) b. _ ( t ) A. _ ( t ) } = { Z. _ ( t ) - μ Z _ ( t ) Z _ ( t ) 3 + A ( t ) b _ ( t ) b _ ( t ) - ω x ( Z _ ( t ) ) - 2 ω x Z. _ ( t ) b _ ( t ) b _ ( t ) A ( t ) b _ ( t ) } s _ ( t + Δ t ) = s _ ( t ) + ∫ t t + Δ t s. _ ( s _ ( t ) ) ⅆ t.
- {umlaut over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
- {dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
- Z(t) is the target position vector (Earth-fixed reference frame);
- μ is the Earth gravitational constant;
- ω is the Earth angular velocity vector;
- Isp is the specific impulse of the target rocket motor;
- gc is the standard gravitational acceleration at Earth's equator; and
- b(t) is the specific mass flow vector of target rocket motor,
- and the target state is expressed as a vector containing at least target position, velocity, specific mass flow rate, and acceleration
- and the derivative of such a vector can be expressed as:
- and the propagation to the end of the current stage is made by integrating the equation
8. A method according to claim 7, wherein said step of integrating is performed using a numerical integration technique such as a fourth order Runge-Kutta scheme.
9. A method according to claim 5, wherein said step of propagating the target hypothesis/stage combination includes the step of, while propagating the hypothesis to the end of the current stage, through subsequent stages, and for a ballistic portion of flight, saving the propagated target state at points sufficiently close in time to completely represent the target trajectory, and making the propagated and saved target states available as the output of the method.
10. A method according to claim 9, wherein said points sufficiently close are one second apart.
11. A method for intercepting a boosting target missile, said method comprising the steps of: Z ¨ _ ( t ) = - μ Z _ ( t ) Z _ ( t ) 3 + A _ ( t ) - ω _ × ( ω _ × Z _ ( t ) ) - 2 ω _ × Z. _ ( t ) gravity thrust centerfugal coriolis A _ ( t ) = I sp g c b _ ( t ) A ( t ) = A ( t ) b. _ ( t ) = b _ ( t ) · b _ ( t ) where s _ ( t ) = { Z _ ( t ) Z. _ ( t ) b _ ( t ) A _ ( t ) } s. _ ( t ) = { Z. _ ( t ) Z ¨ _ ( t ) b. _ ( t ) A. _ ( t ) } = { Z. _ ( t ) - μ Z _ ( t ) Z _ ( t ) 3 + A ( t ) b _ ( t ) b _ ( t ) - ω x ( Z _ ( t ) ) - 2 ω x Z. _ ( t ) b _ ( t ) b _ ( t ) A ( t ) b _ ( t ) } s _ ( t + Δ t ) = s _ ( t ) + ∫ t t + Δ t s. _ ( s _ ( t ) ) ⅆ t
- generating estimates of at least target missile velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), and launch time;
- for each of a plurality of hypotheses of target missile type and stage, obtaining at least the nominal target missile parameters of staging times, specific mass flow rate ({dot over (M)}), specific thrust (ISP), and angle of attack (AoA);
- for each of a plurality of hypotheses of target missile type and stage, computing from said estimated target missile velocity ({circumflex over (V)}mi), position ({circumflex over (X)}mi), and launch time, and from said nominal target missile parameters, an estimate of the current stage, and of the time until burnout of the current stage;
- determining, from said estimates of current stage and time until burnout of current stage the time since ignition of the current stage and then the specific mass flow rate {dot over (M)} at the current time for the target/stage combination;
- for each of said plurality of hypotheses, propagating the target hypothesis/stage combination to a time corresponding to the estimated end time of the current stage, with the assumption being made that the target kinematics are expressed by:
- {umlaut over (Z)}(t) is the target acceleration vector (Earth-fixed reference frame);
- {dot over (Z)}(t) is the target velocity vector (Earth-fixed reference frame);
- Z(t) is the target position vector (Earth-fixed reference frame);
- μ is the Earth gravitational constant;
- ω is the Earth angular velocity vector;
- Isp is the specific impulse of the target rocket motor;
- gc is the standard gravitational acceleration at Earth's equator; and
- b(t) is the specific mass flow vector of target rocket motor,
- and the target state is expressed as a vector containing at least target position, velocity, specific mass flow rate, and acceleration
- and the derivative of such a vector can be expressed as:
- and the propagation to the end of the current stage is made by integrating the following equation using a numerical integration technique such as a fourth order Runge-Kutta scheme
- deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis;
- if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter;
- if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage, and repeating said steps of (a) deciding if the end of the current stage corresponds to the end of the last stage of the hypothesis, (b) if the end of the current stage corresponds to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter and (c) if the end of the current stage does not correspond to the end of the last stage of the hypothesis, propagating the states of the hypothesis through burnout of the current stage; and
- guiding an interceptor to the boosting target missile using the propagated states of the hypothesis.
12. A method according to claim 11, wherein the step of, for each of a plurality of hypotheses of target missile type and stage, computing the time until burnout of the current stage comprises the steps of:
- subtracting the current time from the estimated launch time;
- comparing the resulting estimate of time since target launch to the nominal target timeline for the hypothesis to indicate the stage of the hypothesis.
13. A method according to claim 11, wherein said step of propagating the estimated position and velocity of the target missile to the estimated time of the end of the current stage, through subsequent stages, and for a ballistic portion of flight, includes the step of saving the propagated target state at points sufficiently close in time to completely represent the target trajectory.
14. A method according to claim 13, wherein said step of saving the propagated target state at points sufficiently close in time to completely represent the target trajectory includes the step of saving the propagated target state at points about one second apart.
15. A method according to claim 11, wherein said step of propagating the states of the hypothesis through burnout of the last stage and ballistically thereafter comprises the step of propagating the states until a selected time after lift off (TALO).
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Type: Grant
Filed: May 9, 2006
Date of Patent: Mar 31, 2009
Assignee: Lockheed Martin Corporation (Bethesda, MD)
Inventors: Christian E. Pedersen (Browns Mills, NJ), Jeffrey B. Boka (Lumberton, NJ)
Primary Examiner: Bernarr E Gregory
Attorney: Duane Morris LLP
Application Number: 11/430,535
International Classification: F42B 15/01 (20060101); G06F 19/00 (20060101); F41G 7/00 (20060101);